Biased flow occurs frequently in the slab continuous casting process and leads to downgraded steel quality. A mathematical model has been developed to analyze the three-dimensional biased flow phenomena associated with the effects of static magnetic-field application and argon gas injection in the slab continuous casting process. By moving the submerged entry nozzle (SEN) from center to off-center, the biased flow and vortexing flow in the mold can be reproduced in the numerical simulation. The existence of a vortexing flow is shown to result from three-dimensional biased flow in the mold. A vortex is located at the low-velocity side adjacent to the SEN. The vortex strength depends on the local horizontal velocity of molten steel and decreases gradually with distance from the free surface. The vortexing-zone size depends on the biased distance of the SEN, and the intensity of the vortexing flow depends on the casting speed of the continuous caster. Only when the location and strength of the magnetic field are properly chosen, can the vortexing flow be suppressed by a static magnetic-field application. The effect of argon gas injection on the vortexing flow is not remarkable. The combination of magnetic-field application and argon gas injection can correct the biased flow and suppress the vortexing flow by suppressing the surface velocity and removing the downward velocity near the SEN in the mold.